A280446 -id:A280446 - cp's OEIS frontend

A280445 Consider a number k and all the possible concatenations of the form k = concat(a,b), with a>0. Take the sum of the products of all the pairs a and b, j = Sum{a*b}. Sequence lists the numbers for which j/k is an integer and produce a new record.

655, 5848, 176594, 25820986, 1394797593315

Offset: 1

Paolo P. Lava, Jan 03 2017

The ratios for a(1)-a(5) are 1, 2, 3, 4, and 7, respectively. a(6) > 10^13. - Giovanni Resta, Jan 05 2017

			655 = concat(6,55) = concat(65,5) and (6*55 + 65*5)/655 = 1;
5848 = concat(5,848) = concat(58,48) = concat(584,8) and (5*848 + 58*48 + 584*8)/5848 = 2; etc.

Cf. A280446, A280447.

P:=proc(q) local a,j,k,n; j:=0; for n from 1 to q do a:=0;
for k from 1 to ilog10(n) do a:=a+(n mod 10^k)*trunc(n/10^k); od;
if type(a/n,integer) then if a/n>j then j:=a/n; print(n); fi; fi; od; end: P(10^9);

a(5) from Giovanni Resta, Jan 05 2017

A280447 Like A065759 but where f(n) = 3*n.

Original entry on oeis.org

176594, 281894, 371894, 446594, 1765940, 2818940, 2822594, 3718940, 3722594, 4465940, 17659400, 28189400, 28225940, 37189400, 37225940, 44659400

Offset: 1

Paolo P. Lava, Jan 03 2017

Numbers of the form 176594*10^k, 281894*10^k, 371894*10^k, 446594*10^k, etc., with k>=0, belong to the sequence.

			176594 = concat(1,76594) = concat(17,6594) = concat(176,594) = concat(1765,94) = concat(17659,4) and (1*76594 + 17*6594 + 176*594 + 1765*94 + 17659*4) = 529782 = 3*176594.

Cf. A065759, A280445, A280446.

P:=proc(q) local a,k,n; for n from 1 to q do a:=0;
for k from 1 to ilog10(n) do a:=a+(n mod 10^k)*trunc(n/10^k); od;
if a/n=3 then print(n); fi; od; end: P(10^9);

cp's OEIS Frontend

A280445 Consider a number k and all the possible concatenations of the form k = concat(a,b), with a>0. Take the sum of the products of all the pairs a and b, j = Sum{a*b}. Sequence lists the numbers for which j/k is an integer and produce a new record.

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